A refinement of philosophy, everything can be proven with logic (i.e. -logy, study of correct thinking). Logic even defies go deli and lemons. Although strictly speaking Godel was referring to the limits of math to fully describe itself, not any and everything. The paradox of accepting Godel is that to accept it is to also accept that logic can allow you to accept it, and therefore does confine the limits of Godel’s incompleteness theorem to a subset of all that can be known. And what a shame that we have forgone the basics of logic for such highly specific specialized disciplines that rely on it yet gloss over its importance. Science being the primary example where calling something “philosophical” is seen as a perjorative not worthy of consideration (and heaven forbid that physics consider its philosophical father metaphysics as legitimate).